逾渗理论在多孔介质渗透性能研究中的应用  

Application of Percolation Theory in the Study of Hydraulic Conductivity of Porous Media

作　　者：兰盈伯 程东会[1,2] 项琳 李超[1,2] LAN Ying-bo;CHENG Dong-hui;XIANG Lin;LI Chao(School of Water Resources and Environment,Chang'an University,Xi'an 710054,Shaanxi Province,China;Key Laboratory of Subsurface Hydrology and Ecological Effects in Arid Region,Ministry of Education,Chang′an University,Xi′an 710054,Shaanxi Province,China)

机构地区：[1]长安大学水利与环境学院,陕西西安710054 [2]长安大学旱区地下水文与生态效应教育部重点实验室,陕西西安710054

出　　处：《中国农村水利水电》2024年第8期41-44,53,共5页China Rural Water and Hydropower

基　　金：国家自然科学基金项目(41972248,42372291);陕西省自然科学基础研究计划项目(2019JM-146)。

摘　　要：逾渗现象广泛存在于自然界的各种物理过程中,逾渗理论已经在众多领域得到广泛的应用和研究.区别于传统的以渗透系数为主要参数渗流理论,用逾渗理论表征多孔介质的渗透性能,这可能是解决复杂渗流问题更合理的方法,如当气相侵入饱和多孔介质时,对非混溶的两相流动系统中气相运动的表征。多孔介质可以视为由孔腔与孔喉组成,它们分别对应逾渗网络模型里的节点与连接节点的键,在此概化的基础上逾渗理论可以应用于多孔介质,进而运用逾渗理论中关键路径分析的方法对饱和渗透系数与非饱和渗透系数进行理论推导。以泊肃叶方程为起点,结合连通性以及逾渗临界体积含量等概念,构建出了饱和渗透系数与孔隙临界半径的关系,并在此基础上将孔隙度以孔隙半径的概率密度函数的形式给出并引入平衡半径的概念,加入推导,最终得出非饱和渗透系数的表达式。并使用Rijtema数据库的两种土样实测数据与预测值对比,分析了非饱和渗透系数表达式的适用性。结果发现,给出的非饱和渗透系数的表达式只有在远离逾渗阈值的范围区间内,即饱和度大于0.9时,预测值才与实测值接近,而在小饱和度时,甚至产生了几个数量级误差。这些误差的产生与前述推导过程中的假设与近似处理以及接近逾渗时拓扑的复杂性有关,其结果是越接近临界饱和度,其预测值越不准确。Percolation phenomenon widely exists in various physical processes in natural world,and percolation theory has been widely used and studied in many fields.In contrast to traditional seepage theory taking hydraulic conductivity as the main parameter,percolation theory offers a distinctive approach to understanding the permeability of porous media.This may be a more reasonable approach to solve complex seepage problems such as when the gas phase invades the water-saturated porous medium,the characterization of gas phase motion in immiscible two-phase flow systems in porous media.Porous media,conceptualized as an interconnected network of pores and throats,can be likened to nodes and bond connections in the percolation model.This unique perspective allows the application of percolation theory to porous media,providing a theoretical framework for analyzing both saturated and unsaturated hydraulic conductivities using the critical path analysis method in the percolation theory.The derivation begins with Poiseuille′s equation,a fundamental equation governing fluid flow.Hydraulic conductance and critical volume fraction for percolation become essential concepts in this theoretical exploration.By integrating these concepts with Poiseuille′s equation,the relationship between saturated hydraulic conductivity and critical pore radius is established.To further refine the theoretical framework,on this basis,the porosity is given in the form of a probability density function of the pore radius and the concept of equilibrium radius is introduced into the formula derivation process,this addition enhances the model′s accuracy by accounting for the distribution of pore sizes within the porous media.As a result,the expression for unsaturated hydraulic conductivity finally obtained.The applicability of the unsaturated hydraulic conductivity expression was analyzed by comparing the measured data of two soil samples in the Rijtema database and predicted values.It was found that the expression of the unsaturated hydraulic conduct

关 键 词：逾渗理论 逾渗阈值 饱和渗透系数 非饱和渗透系数 关键路径分析 

分 类 号：TV11[水利工程—水文学及水资源]